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kpad5991

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What is the volume of the solid generated when the area of the curve y=3-3^x is rotated about the x axis
 

HeroWise

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Any ordinates given or assuming first quadrant?


Use the powerful Blue Eyes White logs pls don't kill me
 
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fan96

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What is the volume of the solid generated when the area of the curve y=3-3^x is rotated about the x axis
Infinity.

If bounds are given, use the formula



and use

(for all )

(remember to give your answers in cubic units!)
 
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HeroWise

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Well to summ wat the above posts states is the

x = e ^ (lnx)

is the same thing right?

didnt finish it fully, should be right if i didnt make silly errors, but you want to reach there
 
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dan964

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Herowise one of your coefficients is not correct.

Well to summ wat the above posts states is the

x = e ^ (lnx)

is the same thing right?

didnt finish it fully, should be right if i didnt make silly errors, but you want to reach there
that is some funky integration going on there:

Might be easier to use change of base before integrating. Also maybe leave the exponent as x rather than x+1 before integrating. Less likely to make mistakes that way.
I'll do an improper integral here:






or














This is the improper integral. The integral with limits is done in a similar fashion.
 
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HeroWise

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Pfft i feel dumb, i see where i went wrong, thanks a lot anyway @dan964


EDIT: Wait, no i got the same result as yours @dan964, but i didnt simplify it. if i had, it would come down to your answer, and the ordinates, as i said, im geussing the question is asking for first quadrant, i remember a similar question while going over the Cambridge book, so i just "geussed". That isnt really good but i think the working should suffice the OP
 
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kpad5991

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Herowise one of your coefficients is not correct.



that is some funky integration going on there:

Might be easier to use change of base before integrating. Also maybe leave the exponent as x rather than x+1 before integrating. Less likely to make mistakes that way.
I'll do an improper integral here:






or














This is the improper integral. The integral with limits is done in a similar fashion.
This is what I got you will see the question from the textbook and my solutions I can't seem to get 13c. The books solution is pi(9-8/log3) u^3
https://imgur.com/gallery/u5PCA

Can someone please write the full solution to 13c
 

HeroWise

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Can you tell us the ordinates then, because as the working out provided by both @dan964 and i are elligible, so just put in the ordinates like normal integration, or provide us with ordinates; thatd be helpful for us ty

or send a pic of the whole excercise
 

fan96

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Remember,







 
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